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V. Kinetics of Soil Phosphorus Reactions

V. Kinetics of Soil Phosphorus Reactions

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all rate of this reaction has to some extent been used directly in plant

uptake studies, it has been applied more extensively to subdivide soil

phosphorus into labile and nonlabile fractions and also to subdivide the

labile fraction.



Cooke (1966), using the technique of Amer et al. ( 1955) measured

the rate of release of phosphorus from soil to an anion exchange resin











FIG. 8. Relationship between time and quantity of phosphorus released from

soil to resin. (From Cooke, 1966.)

which acted as a phosphorus sink. He found that for periods up to

about 2 hours, the relationship (Fig. 8 ) between the quantity of phosphorus ( P ) released from the soil and time ( t )was


where b was a constant related to the phosphorus already present in

solution and R was the rate-of-release constant. The rate of release was

shown to be well correlated with plant uptake of phosphorus. The

linear relationship between P and t1Iz was suggested by Cooke and

Larsen (1966) to indicate that the rate of phosphorus release was

controlled by a diffusion step, presumably through the static water

film which surrounds solid particles even when they are stirred in a




Since Russell and his co-workers (1954) introduced the term “labile

soil phosphorus’’ it has been commonly used in soil literature. The

genera1 scientific meaning of the adjective labile is “prone to be displaced or to change,” and for soil phosphorus it is defined as that frac-



tion of the soil phosphorus which can enter the soil solution by isoionic

exchange within an appropriate time span.

Over geological time, all soil phosphorus may be able to enter the

solution phase, but in a restricted time, for example one cropping season,

only a part of the phosphorus is labile. It is therefore necessary to

qualify the word labile with some indication of time span, or the

minimum reaction rate, concerned.

It is obvious that no extractant can remove a labile fraction from

soil, its measurement being possible only by the use of labeled phosphorus. The radioactive isotope 32Phas been available since 1934, and

Mattingly (1957) has given a general review of the use of this isotope

in soil phosphorus work. A clear exposition of the developments in the

use of 32P to determine a labile fraction of soil phosphorus has been

given by Fried (1964), who outlined the various concepts used by

different workers. However contrasting these concepts may be, they are

all based on isotopic dilution analysis, as introduced by Hevesy and

Hobbie ( 1932).

In pure systems, analysis by isotopic dilution involves mixing a small

quantity of labeled material uniformly throughout the system to be

measured. The labeled materia1 must be in the same chemical form as

that to be measured. With intact soil, although the label can be added

as PO, groups, it is impossible to mix these uniformly throughout all

the PO, groups present; indeed, this would only give a measure of total

soil phosphorus. What is measured, is the extent to which the added

label is diluted by exchangeable soil PO, groups. The several methods

of isotopic dilution differ principally in the conditions under which this

dilution occurs. The main concepts are denoted by the terms “surface

phosphorus,” L value, Et value, or A value.

I. Surface Phosphorus

McAuliffe et al. (1948) and later Olsen (1953) believed that the

initial, more rapid, stage of isotopic dilution in a soil suspension involved

only the phosphorus on the surface of solid particles and consequently

named this fraction “surface phosphorus.” The concept of surface

phosphorus is also in accordance with the interpretation Neuman and

Neuman ( 1958) applied to isotopic exchange between hydroxylapatitc

and phosphorus in the solution in which it was suspended. An alternative explanation has recently been put forward by Edgington ( I = ) ,

who advanced the idea that this isotopic dilution was brought about

by a recrystallization mechanism. The concept of surface exchange,

therefore, and its corollary, surface phosphorus, must be reconsidered

(see Section V, C ) . In this context it should be borne in mind that the



close relationship that Olsen (1953) found between the total surface

area of soil and the amount of rapidly isotopically exchangeable phosphorus, does not necessarily mean that the “surface phosphorus” concept

is proved, since the number of minute phosphorus containing crystals

present in a soil may increase with the total surface area.

2. L Value

Larsen (1950, 1952) assumed that the isotopic dilution of the labeled

phosphorus that he added was brought about by a clearly indentifiable

fraction of the soil phosphorus, which he called “exchangeable soil

phosphorus” meaning isotopically exchangeable. He used the time span

of a growing season for dilution to occur and followed its progress by

the changes in the specific activity of phosphorus taken up by a test

crop grown in the labeled soil. He used the equation for isotopic dilution

( Hevesy, 1948):

where C , and C are the specific activities of the applied phosphorus and

plant phosphorus, respectively, X the amount of phosphorus applied,

and y the quantity of soil phosphorus which had taken part in the

isotopic dilution of the applied phosphorus. He found that y was

independent of the amount of phosphorus applied and also became

independent of time, suggesting that isotopic equilibrium was attained.

Russell and his co-workers (1957) studied and modified Larsen’s

technique. They showed that the L value was independent of the amount

of carrier phosphorus, which they varied 1000-fold, and of time of

sampling provided that the attainment of equilibrium was facilitated by

very thorough mixing of the soil with the labeled phosphorus. They

concluded that the best technique was to use “carrier free” 32P, to

prevent chemical reactions between the carrier and the soil, which

might reduce isotopic dilution. They also made a correction for seedborne phosphorus.

In his discussion of E, L, and A values, Fried (1964) defined the

L value as “the amount of phosphorus in the soil and in the soil solution

that is exchangeable with orthophosphate ions added to the soil as

measured by a plant growing in the system.” This definition is correct

as far as it goes, but it also requires reference to the attainment of

isotopic equilibrium. Only when isotopic equilibrium is obtained does

the L value signify a definite quantity of soil phosphorus. If equilibrium

is not attained, the value calculated is not a true L value, although it



can provide an index of “available” phosphorus in soil, Examples of both

these situations are given in Fig. 9.

Although the attainment of a constant L value implies isotopic

equilibrium, it does not necessarily mean that all the isotopic dilution

has occurred in the soil. It is frequently observed that isotopic “equilibrium’’ is reached more rapidly in soils of low phosphorus status,

where the rate of diffusion and exchange would be expected to be slow.






Anderson et al. (1961)









Time, days

FIG.9. Relationship between L value and time showing no equilibrium (Andersen et al., 1961) and attainment of equilibrium (From Larsen and Sutton, 1963).

This may be explained if the 32Pis diluted in the soil with only the most

labile of the labile phosphorus, and the remainder of the isotopic dilution

occurs within the plant. The fact that a constant specific activity is

obtained would suggest that in a time depending on the phosphorus

status of the soil, the plant roots are removing all of a definite fraction

of phosphorus from the limited areas that they are sampling. This

possibility suggests that plants can remove phosphorus only above a

definite energy level, and this is being further investigated in this




3. E Value

Russell et al. (1954) developed the E value as a laboratory equivalent

to the L value. They applied a technique which was similar to that

used by McAuliffe et al. (1948) for the determination of “surface phosphorus” but they made no assumptions concerning the nature of the

phosphorus in the solid phase that was exchanging. They realized that

under laboratory conditions complete isotopic equilibrium is never fully

attained but that after some time the rate of further isotopic dilution

decreased drastically (Fig. 10). Therefore, they chose an arbitrary time

for shaking the suspensions and called their value E t , E for exchangeable

and t for the time of exchange.




Time, days



FIG. 10. Rate of isotopic dilution. (From Russell et at., 1954.)

Although, as stressed by Fried, the L and E values are conceptually

equivalent, identical values are not obtained for a given soil since the

isotopic exchange occurs in two different environments. The E value

refers to a soil suspension from which no phosphorus is removed. The

L value refers to a soil at a moisture level below field capacity; as plants

are grown in the soil, some removal of phosphorus occurs and this may

cause a more extensive dilution than by isotopic exchange alone (Larsen

and Sutton, 1963). The E value has the advantage that it can be easily

and quickly measured, but where the parameter is to be related to

plant uptake of phosphorus, the L value is the more relevant


4. A Value

Fried (1964) defined the A value as “the amount of the available

nutrient in a particular source measured in terms of a fertilizer standard

and based on the assumed definition that if a plant is confronted by two

sources of a nutrient it will take up nutrient from each of these sources in

direct proportion to the amounts available.” He also stressed that to



determine an A value experimentally, the interaction between added

phosphorus and soil should be minimized and the experiment should be

of short enough duration to do this, but long enough to prevent errors

due to the quantity of nutrient in the seed.

Thus by definition, the A value is an availability index for either a

nutrient or a soil and is not a method that depends on reaction rate to

determine a specific phosphorus fraction. However, since labeled phosphorus is used, and the formula for calculating the result is identical to

that used for the L value, some confusion has arisen.


Distinction between A and L Values


Basic requirements






1. Pot experiments

2 . Field experiments

A value

L value

To measure the availability

of soil phosphorus relative to a standard

fertilizer source

To measure the total quantity of plant available

soil phosphorus

A minimum of reaction

between source and soil:

therefore, a short


32Padded with standard

fertilizer source

Sufficient reaction to give

a steady state value:

therefore, a long


32Padded with a minimum

of carrier (to facilitate

exchange with soil


Maximum mixing, no


No mixing, 3nPplaced

Resiilt dependent on degree

of soil exploitation

(equivalent to L value if

all soil in pot is


Can be used to characterize degree of exploitation of soil phosphorus

Result independent of

degree of soil exploitat,ion

Not measurable

Furthermore, the term A value has often been used when it really

is the L value which was determined and some authors have equated

the two by writing L (or A ) values and vice versa. A summary of the

essential differences between L and A values is given in Table IV.



McAuliffe et aE. (1948) observed that the isotopic exchange of

phosphorus between a soil and the solution in which it was suspended



occurred in at least two reaction steps, one fast and one slow. It has

since been common to fractionate isotopically exchangeable soil phosphorus according to the number of reaction steps which could be

deduced by analyzing the relationship between time and the loss of

32Pfrom the solution phase (for example, Talibudeen, 1958).

In all these studies it has been assumed that equilibrium had been

attained between the phosphorus in the solid and liquid phases before

the addition of $*P,and also that the biological activity of the soil suspension had little or no influence. This latter assumption is based on the

work of Goring (1955), who showed that direct szP exchange with


6 00-







Control (aerated)


x Constant C02 (buffer)

o Accumulated C02








Time, hours

FIG. 11. The distribution of "P between solid and liquid phases as a function

of time. (From Larsen, 1967.)

organic soil phosphorus is negligible and that the quantity of 32P incorporated into organic forms by microbial synthesis is small in relation

to that which exchanges with the inorganic phosphorus. Nevertheless,

the influence of metabolic products in general and carbon dioxide in

particular can be of great significance.

The influence of carbon dioxide was studied by Larsen (1967), who

used an experimental technique similar to that of McAuliffe and coworkers except that the carbon dioxide level was varied in two ways;

in the first it was allowed to accumulate and in the second it was kept

approximately constant by connecting the reaction vessel to a carbon

dioxide buffer. A suspension through which atmospheric air was blown

served as control. The results are presented in Fig. 11, in which the

ratio solid-phase 32P:solution-phase STis plotted against reaction time.



This method of presenting the results is identical to the one used by

McAuliffe et al. Although the phosphorus concentration in solution was

little influenced, it may be seen from the graph that the carbon dioxide

level markedly affected the isotopic exchange of soil phosphorus.

McAuliffe et a2. also plotted the same ratio against the logarithm of

time elapsed after 32Paddition and they found a linear relationship for




Accurnulatad CO,

Time, hours,log scale

FIG.12. Results of Fig. 11 replotted on a double logarithmic scale.

the initial part of the curve. However, Larsen (1967) obtained the best

fit of his data when he plotted the logarithm of 32Premaining in solution

against the logarithm of time. He found a good linear fit up to 8 hours

after 32Paddition, after which a second reaction rate became apparent

(Fig. 12). He concluded that this second step was due to a slow net

dissolution of phosphorus so that isotopic exchange occurred against

a concentration gradient. He examined this conclusion by varying the

period of preequilibration of the soil suspension. The results (Fig. 13)



showed a good linear relationship between the logarithm of 32Pin

solution and the logarithm of time for the “nil P addition, 32-day preequilibration” treatment, which was maintained for 256 hours, and there

was no suggestion of a second reaction step. It may also be seen that

where phosphorus had been added, the direction of the apparent second

- -

x 2 days pre-equilibration



P odded


Nil P









Log time, hours

FIG.13. Effect of preequilibration time and phosphorus addition on =P exchange.

(From Larsen, 1967.)

reaction step was reversed. This would result in a slow precipitation of

phosphorus so that the isotopic exchange here occurred with the concentration gradient.

As discussed earlier, McAuliffe et al. and others assumed that the

isotopically exchangeable soil phosphorus was “surface phosphorus”

adsorbed to the soil particles. The double logarithmic relationship

observed by Larsen (1967) suggests that the isotopic exchange is

brought about by a recrystallization mechanism.

Edgington ( 1965), using hydroxylapatite as a model, developed a

rate equation for recrystallization and, on integration of this, obtained

the following power function:

(1 -




+ 7)/7Irb

where (1- a) is the fraction of 3zPremaining in solution at time t, y

is a constant, and b = 1/(n - l ) , where n is related to the order of the

reaction. The value b is obtained directly from the slope of the lines in

Figs. 12 and 13, and hence n can be calculated. Edgington drew attention



to the closeness of the values of n to the number of groups in the crystal

lattice. For a pure hydroxylapatite, Calo(PO,)6(OH)z, he found the

values of n to be 10 for calcium and 7.3 for phosphorus. Consequently,

Larsen took his value of about 5 for phosphorus in a calcareous soil to

be evidence for the presence of a hydroxylapatite deficient in phosphorus.

On phosphorus enrichment of this soil, n increased and approached a

maximum value of about 9.

From these observations, Larsen suggested that the isotopically

exchangeable phosphorus in soil might be present as very small crystals

of hydroxylapatite with a varying content of phosphorus. He also

suggested that these crystals were attached to the surface of soil particles

and that the distinction between adsorbed and precipitated soil phosphorus was immaterial, in that the two concepts arise simply from a

different view of the same system.

It thus seems that at least in neutral and calcareous soils, isotopic

exchange between the liquid and solid phase phosphorus can be explained by a single mechanism and that the lability changes smoothly.

Fractionation of labile phosphorus then has no physical meaning for

these soils, and such separation can only be arbitrary.

A different approach to the study of the reaction kinetics between the

liquid and solid phases was made by Amer et al. ( 1955), who measured

the rate at which an anion-exchange resin took up phosphorus from a

soil suspension. They showed that this rate was independent of the

properties of the resin and depended only on the speed at which phosphorus was dissolved from the solid phase. The relationship found between time and the amount of phosphorus adsorbed by the resin, could

be described by three simultaneous reactions obeying first-order kinetics.

They refrained from naming the sources of the phosphorus involved

in these reactions and preferred to consider them as behavior patterns

characterized by quantity and rate constants. However, it is reasonable

to assume that the very rapid reaction, which was completed within a

few minutes reflected the adsorption of the phosphorus already in the

solution phase. The two slow reactions may be explained if the bulk of

the phosphorus came from calcium phosphates. In Section IV, B, 1 it was

shown that the dissolution of hydroxylapatite may occur via a surface

complex. The formation of this complex is the rate-limiting step, and

this may be what was measured in the second reaction. The third reaction, which was not completed within 3 days, may be an artifact

caused by a gradual buildup of calcium chloride in the solution, which

would depress the solubility of the phosphorus.

A verification of this hypothesis would have to be obtained using

a pure hydroxylapatite/water/resin system.




Mobility of Soil Phosphorus

Soil phosphorus may be moved in three ways: ( a ) by the action of

soil organisms, ( b ) with flowing water (mass flow), ( c ) by thermal

movement along a concentration gradient (diffusion). In each instance

the magnitude of the movement will depend upon the fraction of soil

phosphorus that is involved and the rate of movement of that fraction.


Of the three ways in which phosphorus may be moved, transport

by soil organisms has the most substantial influence. The activity of the

larger soil animals will only cause a random redistribution, whereas

higher plants will bring about a unidirectional movement. The whole of

the labile soil phosphorus is involved in this latter movement and its

mg.P/lOOg. soil








Inorganic P


Organic P


FIG.14. Distribution of phosphorus in an undisturbed profile of a base igneous

till. (From Williams and Saunders, 1956.)

rate will depend upon the quantity of phosphorus which is taken up by

the roots, transported through the plant and released to the topsoil by

subsequent decay. This process may result in a very uneven distribution

of phosphorus in an undisturbed soil profile, for example as found by

Williams and Saunders (19%), see Fig. 14. It can be seen in the figure

that there is a zone of depletion at 20 to 40 inches and a zone of enrichment in the topsoil.

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V. Kinetics of Soil Phosphorus Reactions

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